Problem: Simplify the following expression: $\sqrt{63}+\sqrt{112}+\sqrt{28}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{63}+\sqrt{112}+\sqrt{28}$ $= \sqrt{9 \cdot 7}+\sqrt{16 \cdot 7}+\sqrt{4 \cdot 7}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{7}+\sqrt{16} \cdot \sqrt{7}+\sqrt{4} \cdot \sqrt{7}$ $= 3\sqrt{7}+4\sqrt{7}+2\sqrt{7}$ Finally, simplify by combining the terms. $= ( 3 + 4 + 2 )\sqrt{7} = 9\sqrt{7}$